This invention relates to instruments for measuring heat flux, the rate of transfer of heat energy per unit area.
The Schmidt-Boelter gage, as described in U.S. Pat. No. 1,528,383 issued to E. Schmidt, is a widely accepted measuring instrument for heat flux. It combines high output, small size and good linearity with wide dynamic range. One of its limitations for high speed aero-thermal research is a relatively long response time to rapidly changing heat flux. Attempts by others to improve the response of this gage have encountered two obstacles; the gage output decreases as its response is improved, and the response characteristic exhibits two different time constants. Analysis of the gage output at frequencies close to the frequencies represented by these time constants is difficult or impossible.
Conventional Schmidt-Boelter gage construction and operation are well described by Kidd and Nelson in their monograph How the Schmidt-Boelter Gage Really Works, published by Arnold Engineering Development Center in 1996. FIG. 1, taken from that publication, illustrates typical gage construction. The measuring element is a thermally resistive wafer of aluminum which has been anodized over its entire outer surface to prevent electrical contact with the metallic core during fabrication. The insulated wafer is spirally wound with 35 to 40 turns of 0.051 mm diameter Constantan wire. Then the wound wafer is dipped in a copper plating solution, with the liquid surface approximately on the line A--A. Passage of electroplating current through the wire into the solution causes copper to be deposited on the immersed half of the windings. This makes each turn into a thermocouple pair, with one copper-Constantan (Type T) thermocouple junction on each side of the wafer. The wafer is then cemented into an anodized aluminum housing, its top surface is coated with epoxy, and connections are made to the fine wire. During the encapsulation process it is important to achieve void-free thermal contact between the windings on the bottom of the wafer and the epoxy encapsulant.
When heat flows through the mounted wafer from top to bottom a temperature difference is created across it, and the output voltages of the upper thermocouple junctions become slightly greater than those of the lower junctions. The output voltage across the terminals of the device is the sum of these small voltage differences, and is proportional to the heat flux passing through the wafer.
The thermal time constant of a Schmidt-Boelter gage constructed in this manner will be between 20 and 100 milliseconds. When faster response is needed, the wafer may be made very thin. Time constants of 15 to 20 milliseconds may readily be obtained in this manner. Unfortunately, the response of such gages cannot be improved further without incurring the penalty of second order behavior. Typically, the output of the gage will rise rapidly with a first time constant, and then rise more slowly with a second, longer time constant.
Why does the conventional Schmidt-Boelter behave in this manner? Our analysis indicates that heat passing through the thermally resistive wafer encounters five separate layers of materials with very different thermal properties. The first layer is made up of the upper windings, imbedded in epoxy. The second layer is the alumina created by anodization. The third layer is the wafer of aluminum metal. The fourth layer is alumina created by anodization, and the fifth layer is the bottom windings and epoxy which holds them in place. The temperature difference between the upper and lower windings is actually measured across the middle three elements, two layers of alumina and one of aluminum metal. The sensitivity and the transient response of the gage are mainly produced by the thermal resistance of the two alumina layers.
Measurement of the thermal resistance of an anodized (alumina) layer has proven to be very difficult. About the only conclusion we are confident of is that the resistance is much higher than the bulk properties of alumina would predict. It may be that the stresses between highly crystalline alumina, which has low thermal expansion, and the base metal, which has high thermal expansion, create a physical structure with many dislocations and a rough surface. For whatever reason, the result is a very high thermal resistance.